Measuring the benefits of lying in MARA under egalitarian social welfare
Jonathan Carrero, Ismael Rodriguez, Fernando Rubio
TL;DR
The paper investigates lying incentives in egalitarian MARA by formalizing the allocation problem with additive utilities and introducing the concepts of fake utility and $r$-limited utilities. It employs two-level genetic algorithms (LLGA and ULGA) to approximate the egalitarian solution ${\bf egsol}(A,R,U)$ and search for profitable misreports under unlimited and limited-sum settings. Key findings show that under unlimited settings the best strategy is to substantially underestimate one’s own valuations to secure the $n-m$ top resources, whereas in limited settings no universal lie is reliably beneficial, though adaptive lies can yield small gains when others’ preferences are known with high accuracy. The results imply practical defenses against lying, such as enforcing a constant-sum constraint on reported utilities, with broader implications for robust mechanism design in MARA.
Abstract
When some resources are to be distributed among a set of agents following egalitarian social welfare, the goal is to maximize the utility of the agent whose utility turns out to be minimal. In this context, agents can have an incentive to lie about their actual preferences, so that more valuable resources are assigned to them. In this paper we analyze this situation, and we present a practical study where genetic algorithms are used to assess the benefits of lying under different situations.